Abstract

RISK MANAGEMENT AND CAPITAL ALLOCATION
WITH COHERENT MEASURES OF RISK

Philippe Artzner¹, Freddy Delbaen², Jean­Marc Eber³, David Heath⁴

¹Université Louis Pasteur, Strasbourg
²Eidgenössische Technische Hochschule, Zürich
³Société Générale, Paris
⁴Carnegie Mellon University, Pittsburgh

We present an application of coherent risk measures to the firm­wide risk management of portfolio selection and accounting of risk capital. Both regulators' and shareholders' concerns about use of capital are represented by measuring, under their respective sets of scenarios, expected future net worth and expected future excess of net worth over some required amount. For a firm with many divisions, the decomposition principle in linear optimisation of large scale systems, can be interestingly interpreted via an internal market. Firm's divisions compete internally for capital as well as for risk limits, providing hereby some accounting for risk capital, which is incentive­compatible with decentralized optimisation of the firm's objective. Key words and phrases. accounting for risks, capital allocation, coherent capital assignment, coherent risk measure, concentration of risks, cost allocation, decentralization, decomposition principle, internal trading, measure of risk, net worth, performance measurement, regulators' constraints, risk­based capital, risk management, scenario, shareholders' constraints.